A LevelChemistryAQARevision NotesPhysical ChemistryFormulae, Equations & CalculationsRelative Atomic Mass & Relative Molecular Mass

Relative Atomic Mass & Relative Molecular Mass (AQA A Level Chemistry): Revision Note

Exam code: 7405

Francesca

Written by: Francesca

Reviewed by: Caroline Carroll

Updated on

Relative Atomic Mass Definition

What is Relative Atomic Mass?

Atomic Mass Unit

  • The mass of a single atom is so small that it is impossible to weigh it directly

  • Atomic masses are therefore defined in terms of a standard atom, which is called the unified atomic mass unit

  • This unified atomic mass is defined as one-twelfth of the mass of a carbon-12 isotope

Definition and Formula

  • The relative atomic mass (Ar) of an element is the ratio of the average mass of the atoms of an element to the unified atomic mass unit

  • The relative atomic mass is determined by using the average mass of the isotopes of a particular element

  • The Ar has no units as it is a ratio, and the units cancel each other out

Relative atomic mass of X = fraction numerator bold a bold v bold e bold r bold a bold g bold e bold space bold m bold a bold s bold s bold space bold o bold f bold space bold o bold n bold e bold space bold a bold t bold o bold m bold space bold o bold f bold space bold X over denominator bold o bold n bold e bold space bold t bold w bold e bold l bold f bold t bold h bold space bold o bold f bold space bold t bold h bold e bold space bold space bold m bold a bold s bold s bold space bold o bold f bold space bold o bold n bold e bold space bold c bold a bold r bold b bold o bold n bold minus bold 12 bold space bold a bold t bold o bold m end fraction

Relative isotopic mass

  • The relative isotopic mass is the mass of a particular atom of an isotope compared to the value of the unified atomic mass unit

  • Atoms of the same element with a different number of neutrons are called isotopes

  • Isotopes are represented by writing the mass number as 20Ne, or neon-20, or Ne-20

    • To calculate the average atomic mass of an element, the percentage abundance is taken into account

    • Multiply the atomic mass by the percentage abundance for each isotope and add them all together

    • Divide by 100 to get the average relative atomic mass

    • This is known as the weighted average of the masses of the isotopes

Formula for relative atomic mass: sum of isotope abundance × isotope mass number, divided by 100, where Σ denotes the sum of all isotopes.
The formula for calculating relative atomic mass using percentage abundance and isotopic mass numbers

Relative molecular mass (Mr)

  • The relative molecular mass (Mr) is the ratio of the weighted average mass of a molecule of a molecular compound to the unified atomic mass unit

  • The Mr has no units

Mr = fraction numerator bold w bold e bold i bold g bold h bold t bold e bold d bold space bold a bold v bold e bold r bold a bold g bold e bold space bold m bold a bold s bold s bold space bold o bold f bold space bold m bold o bold l bold e bold c bold u bold l bold e bold s bold space bold i bold n bold space bold a bold space bold g bold i bold v bold e bold n bold space bold s bold a bold m bold p bold l bold e bold space bold o bold f bold space bold a bold space bold m bold o bold l bold e bold c bold u bold l bold a bold r bold space bold c bold o bold m bold p bold o bold u bold n bold d over denominator bold u bold n bold i bold f bold i bold e bold d bold space bold a bold t bold o bold m bold i bold c bold space bold m bold a bold s bold s bold space bold u bold n bold i bold t end fraction

  • The Mr can be found by adding up the relative atomic masses of all atoms present in one molecule

  • When calculating the Mr, the simplest formula for the compound is used, also known as the formula unit

    • Eg., silicon dioxide has a giant covalent structure; however, the simplest formula (the formula unit) is SiO2

Example Mr calculations

Substance 

Atoms present 

Mr

Hydrogen
H2

2 x H

(2 x 1.0) = 2.0

Water
H2O

(2 x H) + (1 x O)

(2 x 1.0) + (1 x 16.0) = 18.0

Potassium carbonate
K2CO3

(2 x K) + (1 x C) + (3 x O)

(2 x 39.1) + (1 x 12.0)
+ (3 x 16.0) = 138.2

Calcium hydroxide
Ca(OH)2

(1 x Ca) + (2 x O) + (2 x H)

(1 x 40.1) + (2 x 16.0)
+ (2 x 1.0) = 74.1

Ammonium sulfate
(NH4)2SO4

(2 x N) + (8 x H) + (1 x S) + (4 x O)

(2 x 14.0) + (8 x 1.0) + (1 x 32.1) + (4 x 16.0) = 132.1

Relative formula mass (Mr)

  • The relative formula mass (Mr) is used for compounds containing ions

  • It has the same units and is calculated in the same way as the relative molecular mass

  • In the table above, the Mr for potassium carbonate, calcium hydroxide, and ammonium sulfate are relative formula masses

Examiner Tips and Tricks

Students often confuse relative atomic mass (Ar) with mass number. Ar is a weighted average across all isotopes, whereas mass number applies to a single isotope.

In percentage abundance calculations, a common error is summing the isotope contributions without dividing by 100 —you should check that your answer is close in magnitude to the individual atomic masses.

Remember that Ar and Mr are dimensionless ratios (no units).


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Francesca

Author: Francesca

Expertise: Chemistry Content Creator

Fran studied for a BSc in Chemistry with Forensic Science, and since graduating taught A level Chemistry in the UK for over 11 years. She studied for an MBA in Senior Leadership, and has held a number of roles during her time in Education, including Head of Chemistry, Head of Science and most recently as an Assistant Headteacher. In this role, she used her passion for education to drive improvement and success for staff and students across a number of subjects in addition to Science, supporting them to achieve their full potential. Fran has co-written Science textbooks, delivered CPD for teachers, and worked as an examiner for a number of UK exam boards.

Caroline Carroll

Reviewer: Caroline Carroll

Expertise: Head of Content Delivery

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about delivering high-quality resources to help students achieve their full potential.